hyper.deal

hyper.deal is an efficient, matrix-free finite-element library for solving partial differential equations in two to six dimensions with high-order discontinuous Galerkin methods. It builds upon the low-dimensional finite-element library deal.II to create low-dimensional meshes and to operate on them individually. We combine these meshes via a tensor product on the fly and provide new special-purpose highly optimized matrix-free functions.

The library hyper.deal is freely available under the LGPL 3.0 license. If you use hyper.deal, please cite the release paper:

@article{munch2020hyperdeal,
  title         = {hyper.deal: An efficient, matrix-free finite-element library for 
                   high-dimensional partial differential equations},  
  author        = {Munch, Peter and Kormann, Katharina and Kronbichler, Martin},
  year          = {2020},
  eprint        = {2020.08110},
  archivePrefix = {arXiv},
  primaryClass  = {cs.MS}
}

The paper has been submitted; the preprint can be found online on arXiv. The full list of publications using or related to hyper.deal can be found here.

We provide following useful resources:

• a WIKI (see here)
• a Doxgen documentation (for building it, see here)
• example programs presenting features of hyper.deal in the folder examples

For getting started, check out the following side.

Authors

The principal developers are (in alphabetical order):

• Katharina Kormann (@kkormann), Max Planck Institute for Plasma Physics and Technical University of Munich, DE
• Martin Kronbichler (@kronbichler), Technical University of Munich, DE
• Peter Munch (@peterrum), Technical University of Munich and Helmholtz-Zentrum Geesthacht, DE

Philosophy

The library hyper.deal is dedicated explicitly only to algorithms for high-dimensional finite-element methods. However, the close ties to deal.II enable us to use general-purpose FEM features from there. In particular, we are contributing to the deal.II project functionalities that have been developed with high-dimensions in mind, but are also useful for lower dimensions.

Via deal.II, we optionally also have access to other third-party libraries like Trilinos, p4est, Metis, or PETSc.

The library hyper.deal is a community development project. Contributions by new developers are more than welcome! In the case of questions, please contact any of the principal developers listed above.